The long term goal of this research is to improve the quality of images in emission and transmission computed tomography by the development of improved statistical methods for reconstruction, as well to investigate improved methodologies for rapid testing and validation of this class of methods. Our focus is on Bayesian statistical methods. Statistical methods have lead to improved image quality relative to filtered backprojection, and this may be attributed to their ability to incorporate models of the imaging system, the noise process, and the spatial properties of the underlying object. In aim 1, we continue our exploration into the technical means for the incorporation of three types of object knowledge: for emission brain studies, (i) spatial properties of the underlying activity (ii) anatomical side information provided by co- registered MR scans (iii) for imaging in the thorax, spatial and tissue-related properties of the attenuation coefficient. Statistical methods are iterative, and issues in reconstruction speed have slowed their adoption. In aim 2, we propose a new class of limited-memory quasi-Newton algorithms, which offer significant speed advantages. Adoption of statistical reconstruction methods is also slowed by the stage of exhaustive testing with digital phantoms; in aim 4 we propose development of theoretical methods that can speed up this step significantly. We hypothesize that conclusions from validation studies with digital phantoms may depend on the detailed verisimilitude of the phantom, and in aim 3 we continue our novel development of realistic digital phantoms based on data from animal autoradiography. Detailed validation studies, some using our newly developed phantoms, are included in aim 5. The proposed work is methodological, but has clinical application in several areas. The structural and anatomical priors of aim 1, as well as the phantoms of aim 3, have particular application to neuro-SPECT and neuro-PET studies, and our development of new transmission algorithms has application attenuation correction in whole body PET oncology and in cardiac SPECT. In aim 5, we continue validation studies with phantoms and retrospective patient data for quantitation and detection tasks using model observers.